If you know So Yong Kim's work at all, chances are you will have her pigeonholed as an archetypal Sundance director with a penchant for investigating her own displaced and fatherless life story. Her first two films, In Between Days (2006) and Treeless Mountain (2008) were studies of, respectively, a teenage Korean girl grappling with a new life in Canada, and two young Korean girls seemingly abandoned by their parents. They won a clutch of festival awards, including a Sundance special jury prize.

But now Kim has made a third film, and it couldn't be more of a U-turn. It's called For Ellen, and is about a stumbling, slurring rock'n'roller, complete with chipped black nail varnish, on the skids and far from home, who staggers into a nameless, snow-covered small town. This musician, Joby Taylor, is on a mission to try and reclaim his six-year-old daughter as his marriage disintegrates and the divorce papers loom. Naturally, it featured at Sundance in 2012 – but for Kim the film represents a lurch towards a higher industry profile.

Principally, this is because she managed to attract Paul Dano as her lead: he gives a staggering performance, a bleary-eyed deadbeat who is also intensely vulnerable. "The English would call him a 'wanker', no?" asks Kim. She's not wrong. "We watched a lot of MTV together, and the Metallica documentary Some Kind of Monster. The way Paul works is to do a lot of preparation. He had to make sure the nail polish was chipped in exactly the right way. Each tattoo had to have a proper story behind it. By the time we came to shoot, there were no questions because he had been so meticulous. All the relationship issues with his wife and girlfriend. Everything."

She and Dano met a few years back, when Dano's partner Zoe Kazan acted in a film directed by Kim's husband Bradley Rust Gray (the couple have two young children). When Kim first sent Dano the script, the character was older, in his mid-30s – "If he had stayed that age, the film would have been quite different, perhaps more hopeless" – and Dano, without actually asking to play the role, suggested the musician should be much younger. "The overall story became more complex, and more accessible."

It was only the final refinement of an idea that had evolved radically from Kim's initial thoughts. "After Treeless Mountain, I wanted to do something completely different. I remembered meeting my own estranged father for the first time when I was six or so – this stranger showed up at our house one day and said, 'I'm your dad.' Then he disappeared." This was when she was still living in Korea (her mother didn't bring her to the US until she was 11), and in her first attempt at writing the For Ellen script, the male character was a ghost, an old man looking back at his life. "After six months of writing, the man had come down in age, to his 30s, and was a conventional guy, a businessman. Then I got stuck. I couldn't get past page 30. I had to put it aside."

Then came a eureka moment: toying with names for the character, she remembered someone called Joby Taylor. "He's a friend from Baltimore – an amazingly spiritual man who was in the Peace Corps for three years, but he has this amazing, rocker-dude name. It fitted perfectly: the character immediately became a musician. We have a lot of musician friends, and they are struggling just like we are: the script just wrote itself after that. I ended up putting all my own anxieties as a film-maker into him, my hang-ups, and what I want to achieve in life."

Having snagged Dano, Kim says he proved invaluable in helping the project along. Credited as "executive producer", he came to investors' meetings, got other actors involved, and added an immense amount of what she calls "texture and depth" to his character.

But with or without him, Kim still had to find someone to play Ellen, the girl at the heart of the story. Having set up camp in Massena, New York, right on the Canadian border, the crew scoured local schools and eventually found six-year-old Shaylena Mandigo in a gym class ("she was one of the smallest kids, but she was so good at focusing and following instructions").

She is now something of an expert at filming with children, having had kids as the central characters of Treeless Mountain – and, in any case, her long-take, low-key shooting style is arguably the best way to film them ("You can't be too precise, and block a scene too exactly"). She describes how she filmed a key scene in a toyshop. "I told Shaylena where to start, and where to finish, and which toy to pick up. I basically set her a task, but had no idea how she would do it. She set her own pace, and we ran the whole magazine of film, about four and half minutes, on the single shot. The scene is as long as could be, and it's as short as it should be."

For Ellen is likely to push Kim's career to a new level. Is she ready for life outside her Sundance comfort zone? "I do have plans," she says, "but I'm struggling with them. I am always asking myself: 'Oh God, I have two kids at home – what am I doing here?' As with Joby, it's a question of priorities."

• For Ellen is released on 15 February. You can watch it from the same date on guardian.co.uk/film